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We present variants of the Conjugate Gradient (CG), Conjugate Residual (CR), and Generalized Minimal Residual (GMRES) methods which are both pipelined and flexible. These allow computation of inner products and norms to be overlapped with…

In our study, a compact third order gas-kinetic scheme is constructed for unstructured grid which is combined the compact least-square reconstruction (CLS) method. The CLS method can achieve arbitrary high order compact reconstruction using…

Shuffling strategies for stochastic gradient descent (SGD), including incremental gradient, shuffle-once, and random reshuffling, are supported by rigorous convergence analyses for arbitrary within-epoch permutations. In particular, random…

This paper describes practical randomized algorithms for low-rank matrix approximation that accommodate any budget for the number of views of the matrix. The presented algorithms, which are aimed at being as pass efficient as needed, expand…

Recent methods utilize graph contrastive Learning within graph-structured user-item interaction data for collaborative filtering and have demonstrated their efficacy in recommendation tasks. However, they ignore that the difference relation…

Biclustering is an unsupervised data mining technique that aims to unveil patterns (biclusters) from gene expression data matrices. In the framework of this thesis, we propose new biclustering algorithms for microarray data. The latter is…

Aiming at improving the performance of existing detection algorithms developed for different applications, we propose a region regression-based multi-stage class-agnostic detection pipeline, whereby the existing algorithms are employed for…

Searching recurrent patterns in complex systems with high-dimensional phase spaces is an important task in diverse fields. In the current work, an improved scheme is proposed to accelerate the recently designed variational approach for…

Augmented Krylov subspace methods aid in accelerating the convergence of a standard Krylov subspace method by including additional vectors in the search space. A residual projection framework based on residual (Petrov-) Galerkin constraints…

One approach for reducing run time and improving efficiency of machine learning is to reduce the convergence rate of the optimization algorithm used. Shuffling is an algorithm technique that is widely used in machine learning, but it only…

We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…

Iterative hybrid projection methods have proven to be very effective for solving large linear inverse problems due to their inherent regularizing properties as well as the added flexibility to select regularization parameters adaptively. In…

Astrochemical simulations are a powerful tool for revealing chemical evolution in the interstellar medium. Astrochemical calculations require efficient processing of large matrices for the chemical networks. The large chemical reaction…

Exponential integrators are time stepping schemes which exactly solve the linear part of a semilinear ODE system. This class of schemes requires the approxima- tion of a matrix exponential in every step, and one successful modern method is…

Back-propagation is a popular machine learning algorithm that uses gradient descent in training neural networks for supervised learning, but can be very slow. A number of algorithms have been developed to speed up convergence and improve…

Biclustering involves the simultaneous clustering of objects and their attributes, thus defining local two-way clustering models. Recently, efficient algorithms were conceived to enumerate all biclusters in real-valued datasets. In this…

Retrosynthesis is the task of breaking down a chemical compound recursively step-by-step into molecular precursors until a set of commercially available molecules is found. Consequently, the goal is to provide a valid synthesis route for a…

Despite the remarkable success of deep learning systems over the last decade, a key difference still remains between neural network and human decision-making: As humans, we cannot only form a decision on the spot, but also ponder,…

By reducing the number of global synchronization bottlenecks per iteration and hiding communication behind useful computational work, pipelined Krylov subspace methods achieve significantly improved parallel scalability on present-day HPC…

Uniform sampling of binary matrix with fixed margins is an important and difficult problem in statistics, computer science, ecology and so on. The well-known swap algorithm would be inefficient when the size of the matrix becomes large or…